In this paper, we consider the problem of finding optimal portfolios in cases when the underlying probability model is not perfectly known. For the sake of robustness, a maximin approach is applied which uses a "confidence set" for the probability distribution. The approach shows the tradeoff between return, risk and robustness in view of the model ambiguity. As a consequence, a monetary value of information in the model can be determined.
A stochastic version of the branch and bound method is proposed for solving stochastic global optimization problems. The method, instead of deterministic bounds, uses stochastic upper and lower estimates of the optimal value of subproblems, to guide the partitioning process. Almost sure convergence of the method is proved and random accuracy estimates derived. Methods for constructing random bounds for stochastic global optimization problems are discussed. The theoretical considerations are illustrated with an example of a facility location problem.
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